Related papers: Strongly Compact Strong Trajectory Attractors for …
In this work, a recently introduced general framework for trajectory statistical solutions is considered, and the question of convergence of families of such solutions is addressed. Conditions for the convergence are given which rely on…
The global attractor conjecture says that toric dynamical systems (i.e., a class of polynomial dynamical systems on the positive orthant) have a globally attracting point within each positive linear invariant subspace -- or, equivalently,…
This article is devoted to the study of multivalued semigroups and their asymptotic behavior, with particular attention to iterations of set-valued mappings. After developing a general abstract framework, we present an application to a time…
This work is concerned with new results on long-time dynamics of a class of hyperbolic evolution equations related to extensible beams with three distinguished nonlocal nonlinear damping terms. In the first possibly degenerate case, the…
We consider a model for the evolution of a mixture of two incompressible and partially immiscible Newtonian fluids in two dimensional bounded domain. More precisely, we address the well-known model H consisting of the Navier-Stokes equation…
We prove that the weakly damped cubic Schr\"odinger flow in $L^2(\T)$ provides a dynamical system that possesses a global attractor. The proof relies on a sharp study of the behavior of the associated flow-map with respect to the weak $…
This paper investigates the longtime behavior of delayed 3D Navier-Stokes equations in terms of attractors. The study will strongly rely on the investigation of the linearized Navier-Stokes system, and the relationship between the discrete…
We investigate whether early and late time attractors for non-conformal kinetic theories exist by computing the time-evolution of a large set of moments of the one-particle distribution function. For this purpose we make use of a previously…
This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of $\mathbb{R}^3$ with cubic nonlinear terms and locally distributed damping. The existence of regular finite-dimensional global…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
We consider a hydrodynamic system that models the Smectic-A liquid crystal flow. The model consists of the Navier-Stokes equation for the fluid velocity coupled with a fourth-order equation for the layer variable $\vp$, endowed with…
Takens' Embedding Theorem remarkably established that concatenating M previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state…
We investigate the analyticity of the attractors of a class of Kuramoto-Sivashinsky type pseudo-differential equations in higher dimensions, which are periodic in all spatial variables and possess a universal attractor. This is done by…
In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…
This paper is a sequel to Chaika and Krishnan [arXiv:1612.00434]. We again consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice Z^d. We assume that once walks meet, they…
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying…
We propose a modification technique for discrete time systems for exponentially fast convergence to compact sets. The extension technique allows us to use tools defined on Euclidean spaces to systems evolving on manifolds by modifying the…
As in our previous paper, the 3D Navier-Stokes equations with a translationally bounded force contain pullback attractors in a weak sense. Moreover, those attractors consist of complete bounded trajectories. In this paper, we present a…
We study the long-term behavior of the distribution of the solution process to the non-autonomous McKean-Vlasov stochastic delay lattice system defined on the integer set $\mathbb{Z}$. Specifically, we first establish the well-posedness of…
We prove the existence of a compact, finite dimensional, global attractor for a coupled PDE system comprising a nonlinearly damped semilinear wave equation and a nonlinear system of thermoelastic plate equations, without any mechanical…